Sub-isomorph-free subgroup
From Groupprops
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
A subgroup of a group
is termed a sub-isomorph-free subgroup if there exists an ascending chain of subgroups:
such that each is an isomorph-free subgroup of
.
Effect of property operators
In terms of the subordination operator
This property is obtained by applying the subordination operator to the property: isomorph-free subgroup
View other properties obtained by applying the subordination operator
Relation with other properties
Stronger properties
Weaker properties
- Sub-(isomorph-normal characteristic) subgroup
- Left-transitively WNSCDIN-subgroup
- Characteristic subgroup
- Normal subgroup
Metaproperties
Transitivity
This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity